Supplementing Missing Self-Reported Race Data with a Probability Distribution in Logistic Regression Models
Bibliographic record
Abstract
Race is often included as an independent variable in health services research, especially in recent studies of racial and ethnic disparities in health care. Although self-reported information on race exists in large electronic health records (EHR) data, these data are sometimes missing. Recently Bayesian Improved Surname Geocoding method (BISG) is used to estimate the probability distribution of race categories for those with missing information on race. The BISG estimated probability distribution has been used in reporting health care measures but not in statistical modellings with dichotomous events as outcomes. We propose two approaches to accommodate available distribution probability of an independent categorical variable (e.g., race) in logistic regression models: 1) a direct substitution approach and 2) a partial information maximum likelihood estimator (PIMLE). In examining the association between race and up-to-date immunization status of children by three years old from an integrated health care organization, 11.3% of 14,903 children have missing self-reported race information but have BISG estimated probability distribution for the six race/ethnicity categories. We employed the direct substitution approach and PIMLE approach to analyze the under vaccination data. Both approaches included all observations and thus yielded smaller standard errors of estimated coefficients compared to the complete data analyses. Our simulation study showed that the direct substitution approach and PIMLE yielded nearly unbiased coefficient estimates and preserved efficiency when the missing rate of the independent categorical variable was up to 30%.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.037 | 0.115 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".